SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE Hwang, Seung-Su;
It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is isometric to a standard sphere. In this paper we investigate the relationship between the first Betti number and stable minimal surfaces, and study the analytic properties of stable minimal surfaces in M for n = 3.
total scalar curvature;critical points;stable minimal surfaces;